The potential at an axial point (P1) is
If d << r then
V = (1/4pe0)(p/r2)
where p = qd is the dipole moment
The potential at an equatorial point (P2)
V = 0
The potential at any arbitrary point (P3, located at r, q coordinates) is (for r >> d)
V = (1/4pe0).(pcosq/r2)
Potential at a point which is equidistant from +q and Ėq charge is zero. Thus potential at all points
lying on the equatorial plane is zero for a dipole.